Geometry & Topology
- Geom. Topol.
- Volume 22, Number 1 (2018), 305-322.
Chord arc properties for constant mean curvature disks
We prove a chord arc type bound for disks embedded in with constant mean curvature that does not depend on the value of the mean curvature. This bound is inspired by and generalizes the weak chord arc bound of Colding and Minicozzi in Proposition 2.1 of Ann. of Math. 167 (2008) 211–243 for embedded minimal disks. Like in the minimal case, this chord arc bound is a fundamental tool for studying complete constant mean curvature surfaces embedded in with finite topology or with positive injectivity radius.
Geom. Topol., Volume 22, Number 1 (2018), 305-322.
Received: 4 November 2015
Revised: 12 March 2017
Accepted: 9 April 2017
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 49Q05: Minimal surfaces [See also 53A10, 58E12] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Meeks, William; Tinaglia, Giuseppe. Chord arc properties for constant mean curvature disks. Geom. Topol. 22 (2018), no. 1, 305--322. doi:10.2140/gt.2018.22.305. https://projecteuclid.org/euclid.gt/1513774914